We estimate scaled seismic energy and apparent stress to explore the relationship between radiated seismic energy and moment. Our empirical Green's function method uses time-averaged coda spectra, to exploit the stability and averaging effects of the seismic coda. In each region, we choose events that are nearly co-located so that the path term to any station is constant. Small events are used as empirical Green's functions to correct for propagation effects. For eight sequences in the western US, Mexico and Honshu, Japan, over 8 orders of seismic moment, we find that the apparent stress averages to 1 MPa for most events, with scatter between particular events and sequences. Overall, our results support earthquake self-similarity, and are consistent with studies of radiated energy determined by other methods; however, we identify several earthquakes in the magnitude range of Mw 4.5 to Mw 5.5 in Japan that have anomalously high (10 MPa) and low (20 KPa) apparent stress. We investigate the source of these energized and enervated earthquakes, their spectra, and their acceleration records. The enervated events are depleted in high frequencies compared to regular events of similar size, while the energetic events are enhanced in higher frequencies. These earthquakes highlight the fact that real variations in apparent stress exist, even though there is no systematic variation in apparent stress with earthquake size for large populations. A better understanding of the conditions that lead to these anomalous events should aid in the understanding of the origin of high frequency ground motion and may help place constraints on levels of extreme ground motion prediction.